The present invention relates generally to bridges. In particular, this invention relates to a truss for redistributing and reducing the bending moment of a girder, and furthermore, reducing the deflection of the girder.
Bridge design has developed into three basic categories in an effort to decrease the size and cost of the bridge and its supporting xe2x80x9cbridgeworksxe2x80x9d for long bridge spans. The three basic categories are trussed spans and arches, suspension spans, and beam, box and T girders. Trussed span and arches are generally used for supporting two types of structures, bridges and roof frames. The different types of bridge trusses include Warren bridge trusses, Howe bridge trusses, and Pratt bridge trusses. The different types of roof frame trusses include Belgian trusses, Fink trusses, Howe trusses, Pratt trusses, Crecent trusses, Fan trusses, and Scissor trusses. These conventional trussed span and arch designs employ pin-jointed lattice frameworks composed of tension and compression members. The different trussed span frameworks, although complex, obtain their strength from the simple geometric rigidity of the triangle. These conventional trussed span framework designs are composed of straight tension and compression members which extend the length of the bridge span as a uniform assembly of chords resolving loads and moments at each framework joint. Since the rigidity of the trussed span and arch framework is secured by triangles which cannot deform without changing the length of the sides, it is generally assumed that loads applied at the panel points or joint will only produce direct stress. Thus, trusses with large vertical height or depth can be designed to resist vertical loads more efficiently using trussed span and arches than beam, box or T girders.
Due to the complexity of the trussed span and arch frame work, trussed span and arches are used in bridge design only when long spans are required. The Warren bridge truss is generally thought to be the most economical of the trussed span and arch designs. A typical Warren bridge truss 100 is shown in FIG. 1. The Warren bridge truss 100 is comprised of a top chord 105, a bottom chord 110, vertical web members 115, and diagonal web members 120. Web members 115 and 120 form the basic triangular geometry 125 common to all trussed span and arch bridge designs. The joint 130 rigidity of each triangular section resists the load applied to the bottom chord 110 of the Warren bridge truss 100. In conventional applications, the depth of the Warren bridge truss 100 to the length of the bridge span is usually between 1:5 and 1:10. Thus, for a bridge span of 60 feet, the height of the top chord 105 of the Warren bridge truss 100 structure above the bottom chord 110 is from 6 to 12 feet. When a load is applied to a bottom chord 110 between the joints 130, the bottom chord 110 does not directly interact with the primary truss diagonal and vertical lacing of the Warren bridge truss 100. Instead, the load is distributed by beam action of the bottom chord 110 to the adjacent joints 130.
Roof trusses are generally different from bridge trusses because roofs are often pitched, meaning that the top chord of the truss is set at an angle to the horizontal. Roof trusses are designed to support loads which are applied to the top chord of the roof and to accommodate the functionality of the roof as a surface which drains or sheds water, snow or other fluid loads. The bottom chord of the roof truss is considered to be axially loaded, not subjected to beam action where the member bends. A typical Belgian roof truss 200 is shown in FIG. 2. This shows the top chord 205 pitched to the horizontal, a horizontal bottom chord 210, parallel vertical members 215 and diagonal members 220. The parallel vertical members 215 and the diagonal members 220 comprise the web members of the Belgian roof truss 200.
A typical variation of the Belgian roof truss 200 is shown in FIG. 3 where it is used as a bridge truss. This variation shown in FIG. 3 eliminates all diagonal members 220, and may eliminate all vertical members 215 shown in FIG. 2, except the vertical member 315 at the bridge midpoint 320. The variation shown in FIG. 3 offers support to the bottom chord 310 by creating an upwards reaction in member 315 due to the compressive loads in the diagonal members 305. This upwards reaction at member 315 modifies the downwards load which the bottom chord 310 experiences, and consequentially modifies the strain and stress of the beam action in the bottom chord 310. According to trussed framed theory, the load applied to the bottom chord 310 between joints 325 is distributed to the joints 325 by beam action for the beam length between the bottom chord 310 end points and midpoint 320. However, using the theory of work, strain energy in the bottom chord 310 is modified by the reaction at the joint 325 located at the bottom chord 310 midpoint 320 and the length of the beam between end points 330 and 335.
The second type of bridge design is a suspension span. Suspension spans utilize cable networks suspended from arches or towers to connect to and support a bridge roadway. The suspension cables serve as multiple support points for the roadway span and effectively reduce the size of the overall bridge structure. The arch or towers serve as the main support for the bridge span. The roadway can either be a beam girder or trussed structure.
The third type of bridge design is a beam, box and T girder. Beam, box and T girder bridge spans involve a structural shape, or combination of shapes, which has a section modulus and moment of inertia that supports the design load between the unsupported length of the span. Beam girder bridges rely upon the bending of the beam, or xe2x80x9cbeam actionxe2x80x9d to support the bridge load. When a beam is subjected to a load, it bends in the plane of the load. This bending action creates fields of stresses which resist the bending and create an equilibrium condition. For example, a simple beam supported at each end which bends down under a load is experiencing a shortening of the top (or concave surface), and a lengthening of the bottom (or convex surface). These changes in the beam""s shape create horizontal tensile and compressive stresses at the beam""s surfaces. In order for these beam""s two surfaces to work together, vertical shear is developed in the beam web, which is the section located between the top and bottom of the beam. The internal moment developed in the beam section by the horizontal and vertical stresses, generally called xe2x80x9cbeam actionxe2x80x9d, resists the external bending moment of the applied load. The external bending moment calculated by summing the moments of the external forces acting at either end of the beam.
Beam girders for bridge spans are preferred over trussed span and arches or suspension spans because of their simplicity. A compact beam girder is an efficient system which transfers shear and load between the extreme upper and lower elements, in most cases flanges, of the beam. This is especially true for a rolled beam section, such as an I beam. The compact beam section of an I beam functions as a complete system requiring little or no modification in order to support its calculated load. However, for a beam, box or T girder design having a uniformly applied load per foot, the bending moment increases by the square of the span. This can cause very large increases in girder beam size with relatively small increases in span. Thus, when designing a bridge using a beam, box or T girder, the structural requirements of the girder are determined by merely adjusting the size of the girder to fit the design constraints (stress or deflection) until the size of the girder becomes so large and expensive that a shift to the more complex trussed span and arch or suspended bridge designs becomes practicable.
In the large majority of cases, bridge girder size is also determined by deflection criteria rather than limitations on beam stress. Deflection criteria are usually expressed as an allowable vertical deflection per foot of bridge span. For example, a 1:350 deflection criterion would require that a bridge girder not deflect more than 1 foot for every 350 feet under a design load. Deflection criteria from 1:800 up to 1:1200 are common in both vehicular and pedestrian bridge girder designs. Hence deflection limitations often dominate bridge girder design, defeating the economy of higher-strength steels which allow greater stress levels than the same cross-section of mild steels. There is no conventional truss design that utilizes a compact truss system which compares to the simple cross section of a beam girder. Each truss system design requires multiple connections, lacings and chords, which complicate and increase construction and erection costs.
The present invention provides a truss for enhancing a girder that substantially eliminates or reduces disadvantages and problems associated with previously developed girder enhancing trusses.
More specifically, the present invention provides a truss for distributing a maximum bending moment normally occurring at a midpoint region of a girder having first and second ends and a uniform applied load. The truss for distributing a maximum bending moment normally occurring at a midpoint region of a girder includes a first truss segment member having first and second ends, a second truss segment member having first and second ends, a third truss segment member having first and second ends, a fourth truss segment member having first and second ends, and a fifth truss segment member having first and second ends. The first end of the first truss segment member is attached substantially perpendicular to the girder at a first location near the midpoint region of the girder. The first end of the second truss segment member is attached at the midpoint region of the girder and the second end of the second truss segment member is attached to the second end of the first truss segment member. The first end of the third truss segment member is attached substantially perpendicular to the girder at a second location near the midpoint region of the girder. The first location is located between the second location and the first end of the girder. The first end of the fourth truss segment member is attached at the midpoint region of the girder and the second end of the fourth truss segment member is attached to the second end of the third truss segment member. The first end of the fifth truss segment member is attached to the second end of the first truss segment member and the second end of the fifth truss segment member is attached to the second end of the third truss segment member. An upward force is applied to the second ends of the first and third truss segment members to distribute the maximum bending moment of the girder toward the ends of the girder. A first positive maximum bending moment of the girder occurs between the first end of the girder and the first location and a second positive maximum bending moment of the girder occurs between a second end of the girder and the second location.
The present invention provides an important technical advantage by providing a truss design that reduces the required size and material weight of a bridge girder for any given span by a factor of three or more over conventional bridge girder designs.
The present invention provides another important technical advantage by providing a truss design that reduces the deflection at the midpoint of a girder by a factor of four or more over conventional bridge girder designs.
The present invention provides yet another important technical advantage by providing a truss design that significantly reduces bridge girder design costs for any given span.
The present invention provides yet another important technical advantage by providing a truss which embodies a capacity for increased weight at the midpoint of the bridge girder design so road expansions, rest areas, turn-arounds, or parking areas can be constructed at the girder midpoint.